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[K3BHPD1] - Regression with a Dense Network (DNN)¶

Simple example of a regression with the dataset Boston Housing Prices Dataset (BHPD)

Objectives :¶

  • Predicts housing prices from a set of house features.
  • Understanding the principle and the architecture of a regression with a dense neural network

The Boston Housing Prices Dataset consists of price of houses in various places in Boston.
Alongside with price, the dataset also provide theses informations :

  • CRIM: This is the per capita crime rate by town
  • ZN: This is the proportion of residential land zoned for lots larger than 25,000 sq.ft
  • INDUS: This is the proportion of non-retail business acres per town
  • CHAS: This is the Charles River dummy variable (this is equal to 1 if tract bounds river; 0 otherwise)
  • NOX: This is the nitric oxides concentration (parts per 10 million)
  • RM: This is the average number of rooms per dwelling
  • AGE: This is the proportion of owner-occupied units built prior to 1940
  • DIS: This is the weighted distances to five Boston employment centers
  • RAD: This is the index of accessibility to radial highways
  • TAX: This is the full-value property-tax rate per 10,000 dollars
  • PTRATIO: This is the pupil-teacher ratio by town
  • B: This is calculated as 1000(Bk — 0.63)^2, where Bk is the proportion of people of African American descent by town
  • LSTAT: This is the percentage lower status of the population
  • MEDV: This is the median value of owner-occupied homes in 1000 dollars

What we're going to do :¶

  • Retrieve data
  • Preparing the data
  • Build a model
  • Train the model
  • Evaluate the result

Step 1 - Import and init¶

You can also adjust the verbosity by changing the value of TF_CPP_MIN_LOG_LEVEL :

  • 0 = all messages are logged (default)
  • 1 = INFO messages are not printed.
  • 2 = INFO and WARNING messages are not printed.
  • 3 = INFO , WARNING and ERROR messages are not printed.
In [1]:
import os
os.environ['KERAS_BACKEND'] = 'torch'

import keras

import numpy as np
import matplotlib.pyplot as plt
import pandas as pd
import os,sys

import fidle

# Init Fidle environment
run_id, run_dir, datasets_dir = fidle.init('K3BHPD1')


FIDLE - Environment initialization

Version              : 2.3.2
Run id               : K3BHPD1
Run dir              : ./run/K3BHPD1
Datasets dir         : /lustre/fswork/projects/rech/mlh/uja62cb/fidle-project/datasets-fidle
Start time           : 22/12/24 21:20:59
Hostname             : r3i6n0 (Linux)
Tensorflow log level : Info + Warning + Error  (=0)
Update keras cache   : False
Update torch cache   : False
Save figs            : ./run/K3BHPD1/figs (True)
keras                : 3.7.0
numpy                : 2.1.2
sklearn              : 1.5.2
yaml                 : 6.0.2
matplotlib           : 3.9.2
pandas               : 2.2.3
torch                : 2.5.0

Verbosity during training :

  • 0 = silent
  • 1 = progress bar
  • 2 = one line per epoch
In [2]:
fit_verbosity = 1

Override parameters (batch mode) - Just forget this cell

In [3]:
fidle.override('fit_verbosity')

** Overrided parameters : **
fit_verbosity        : 2

Step 2 - Retrieve data¶

2.1 - Option 1 : From Keras¶

Boston housing is a famous historic dataset, so we can get it directly from Keras datasets

In [4]:
# (x_train, y_train), (x_test, y_test) = keras.datasets.boston_housing.load_data(test_split=0.2, seed=113)

2.2 - Option 2 : From a csv file¶

More fun !

In [5]:
data = pd.read_csv(f'{datasets_dir}/BHPD/origine/BostonHousing.csv', header=0)

display(data.head(5).style.format("{0:.2f}").set_caption("Few lines of the dataset :"))
print('Missing Data : ',data.isna().sum().sum(), '  Shape is : ', data.shape)
Few lines of the dataset :
  crim zn indus chas nox rm age dis rad tax ptratio b lstat medv
0 0.01 18.00 2.31 0.00 0.54 6.58 65.20 4.09 1.00 296.00 15.30 396.90 4.98 24.00
1 0.03 0.00 7.07 0.00 0.47 6.42 78.90 4.97 2.00 242.00 17.80 396.90 9.14 21.60
2 0.03 0.00 7.07 0.00 0.47 7.18 61.10 4.97 2.00 242.00 17.80 392.83 4.03 34.70
3 0.03 0.00 2.18 0.00 0.46 7.00 45.80 6.06 3.00 222.00 18.70 394.63 2.94 33.40
4 0.07 0.00 2.18 0.00 0.46 7.15 54.20 6.06 3.00 222.00 18.70 396.90 5.33 36.20 
Missing Data :  0   Shape is :  (506, 14)

Step 3 - Preparing the data¶

3.1 - Split data¶

We will use 70% of the data for training and 30% for validation.
The dataset is shuffled and shared between learning and testing.
x will be input data and y the expected output

In [6]:
# ---- Shuffle and Split => train, test
#
data       = data.sample(frac=1., axis=0)
data_train = data.sample(frac=0.7, axis=0)
data_test  = data.drop(data_train.index)

# ---- Split => x,y (medv is price)
#
x_train = data_train.drop('medv',  axis=1)
y_train = data_train['medv']
x_test  = data_test.drop('medv',   axis=1)
y_test  = data_test['medv']

print('Original data shape was : ',data.shape)
print('x_train : ',x_train.shape, 'y_train : ',y_train.shape)
print('x_test  : ',x_test.shape,  'y_test  : ',y_test.shape)

Original data shape was :  (506, 14)
x_train :  (354, 13) y_train :  (354,)
x_test  :  (152, 13) y_test  :  (152,)

3.2 - Data normalization¶

Note :

  • All input data must be normalized, train and test.
  • To do this we will subtract the mean and divide by the standard deviation.
  • But test data should not be used in any way, even for normalization.
  • The mean and the standard deviation will therefore only be calculated with the train data.
In [7]:
display(x_train.describe().style.format("{0:.2f}").set_caption("Before normalization :"))

mean = x_train.mean()
std  = x_train.std()
x_train = (x_train - mean) / std
x_test  = (x_test  - mean) / std

display(x_train.describe().style.format("{0:.2f}").set_caption("After normalization :"))
display(x_train.head(5).style.format("{0:.2f}").set_caption("Few lines of the dataset :"))

x_train, y_train = np.array(x_train), np.array(y_train)
x_test,  y_test  = np.array(x_test),  np.array(y_test)
Before normalization :
  crim zn indus chas nox rm age dis rad tax ptratio b lstat
count 354.00 354.00 354.00 354.00 354.00 354.00 354.00 354.00 354.00 354.00 354.00 354.00 354.00
mean 3.48 12.46 10.77 0.06 0.55 6.27 67.49 3.89 9.24 401.92 18.36 359.05 12.53
std 8.70 24.44 6.85 0.25 0.12 0.71 28.69 2.07 8.56 167.22 2.17 88.87 7.26
min 0.01 0.00 0.46 0.00 0.39 3.56 2.90 1.17 1.00 188.00 12.60 0.32 1.92
25% 0.08 0.00 4.95 0.00 0.45 5.89 42.32 2.11 4.00 277.50 16.92 376.78 6.74
50% 0.22 0.00 8.14 0.00 0.53 6.21 76.25 3.46 5.00 329.00 18.80 392.05 10.59
75% 2.81 20.00 18.10 0.00 0.62 6.61 93.57 5.37 8.00 666.00 20.20 396.90 16.95
max 88.98 100.00 27.74 1.00 0.87 8.70 100.00 10.71 24.00 711.00 21.20 396.90 36.98
After normalization :
  crim zn indus chas nox rm age dis rad tax ptratio b lstat
count 354.00 354.00 354.00 354.00 354.00 354.00 354.00 354.00 354.00 354.00 354.00 354.00 354.00
mean 0.00 0.00 0.00 -0.00 -0.00 -0.00 -0.00 -0.00 0.00 -0.00 0.00 0.00 0.00
std 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
min -0.40 -0.51 -1.50 -0.26 -1.37 -3.81 -2.25 -1.31 -0.96 -1.28 -2.65 -4.04 -1.46
25% -0.39 -0.51 -0.85 -0.26 -0.89 -0.54 -0.88 -0.86 -0.61 -0.74 -0.66 0.20 -0.80
50% -0.37 -0.51 -0.38 -0.26 -0.16 -0.09 0.31 -0.21 -0.49 -0.44 0.20 0.37 -0.27
75% -0.08 0.31 1.07 -0.26 0.64 0.48 0.91 0.72 -0.14 1.58 0.85 0.43 0.61
max 9.83 3.58 2.48 3.79 2.78 3.42 1.13 3.29 1.72 1.85 1.31 0.43 3.37
Few lines of the dataset :
  crim zn indus chas nox rm age dis rad tax ptratio b lstat
319 -0.34 -0.51 -0.13 -0.26 -0.05 -0.23 -0.30 0.06 -0.61 -0.59 0.02 0.42 0.03
255 -0.40 2.76 -1.04 -0.26 -1.37 -0.56 -1.69 2.57 -0.96 -0.52 -0.90 0.41 -0.45
455 0.15 -0.51 1.07 -0.26 1.41 0.35 0.66 -0.70 1.72 1.58 0.85 -3.47 0.77
414 4.86 -0.51 1.07 -0.26 1.24 -2.47 1.13 -1.08 1.72 1.58 0.85 -3.05 3.37
86 -0.39 -0.51 -0.92 -0.26 -0.88 -0.36 -0.78 0.26 -0.73 -0.93 0.07 0.42 0.05

Step 4 - Build a model¶

About informations about :

  • Optimizer
  • Activation
  • Loss
  • Metrics
In [8]:
def get_model_v1(shape):
  
  model = keras.models.Sequential()
  model.add(keras.layers.Input(shape, name="InputLayer"))
  model.add(keras.layers.Dense(32, activation='relu', name='Dense_n1'))
  model.add(keras.layers.Dense(64, activation='relu', name='Dense_n2'))
  model.add(keras.layers.Dense(32, activation='relu', name='Dense_n3'))
  model.add(keras.layers.Dense(1, name='Output'))
  
  model.compile(optimizer = 'adam',
                loss      = 'mse',
                metrics   = ['mae', 'mse'] )
  return model

Step 5 - Train the model¶

5.1 - Get it¶

In [9]:
model=get_model_v1( (13,) )

model.summary()

# img=keras.utils.plot_model( model, to_file='./run/model.png', show_shapes=True, show_layer_names=True, dpi=96)
# display(img)

Model: "sequential"

┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━┓
┃ Layer (type)                         ┃ Output Shape                ┃         Param # ┃
┡━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━┩
│ Dense_n1 (Dense)                     │ (None, 32)                  │             448 │
├──────────────────────────────────────┼─────────────────────────────┼─────────────────┤
│ Dense_n2 (Dense)                     │ (None, 64)                  │           2,112 │
├──────────────────────────────────────┼─────────────────────────────┼─────────────────┤
│ Dense_n3 (Dense)                     │ (None, 32)                  │           2,080 │
├──────────────────────────────────────┼─────────────────────────────┼─────────────────┤
│ Output (Dense)                       │ (None, 1)                   │              33 │
└──────────────────────────────────────┴─────────────────────────────┴─────────────────┘

 Total params: 4,673 (18.25 KB)

 Trainable params: 4,673 (18.25 KB)

 Non-trainable params: 0 (0.00 B)

5.2 - Train it¶

In [10]:
history = model.fit(x_train,
                    y_train,
                    epochs          = 60,
                    batch_size      = 10,
                    verbose         = fit_verbosity,
                    validation_data = (x_test, y_test))

Epoch 1/60

36/36 - 1s - 33ms/step - loss: 552.6011 - mae: 21.6340 - mse: 552.6011 - val_loss: 459.5090 - val_mae: 19.4499 - val_mse: 459.5090

Epoch 2/60

36/36 - 0s - 8ms/step - loss: 318.6428 - mae: 15.4018 - mse: 318.6428 - val_loss: 137.6176 - val_mae: 9.1210 - val_mse: 137.6176

Epoch 3/60

36/36 - 0s - 8ms/step - loss: 70.6390 - mae: 6.3921 - mse: 70.6390 - val_loss: 58.6480 - val_mae: 5.6008 - val_mse: 58.6480

Epoch 4/60

36/36 - 0s - 8ms/step - loss: 39.1765 - mae: 4.6129 - mse: 39.1765 - val_loss: 41.4944 - val_mae: 4.7192 - val_mse: 41.4944

Epoch 5/60

36/36 - 0s - 8ms/step - loss: 29.0254 - mae: 3.9321 - mse: 29.0254 - val_loss: 33.0362 - val_mae: 4.1499 - val_mse: 33.0362

Epoch 6/60

36/36 - 0s - 8ms/step - loss: 24.0055 - mae: 3.5411 - mse: 24.0055 - val_loss: 28.8925 - val_mae: 3.8650 - val_mse: 28.8925

Epoch 7/60

36/36 - 0s - 8ms/step - loss: 21.0437 - mae: 3.2821 - mse: 21.0437 - val_loss: 26.5158 - val_mae: 3.6375 - val_mse: 26.5158

Epoch 8/60

36/36 - 0s - 8ms/step - loss: 18.8576 - mae: 3.1259 - mse: 18.8576 - val_loss: 24.8119 - val_mae: 3.5243 - val_mse: 24.8119

Epoch 9/60

36/36 - 0s - 8ms/step - loss: 17.1906 - mae: 3.0018 - mse: 17.1906 - val_loss: 23.7083 - val_mae: 3.3951 - val_mse: 23.7083

Epoch 10/60

36/36 - 0s - 8ms/step - loss: 16.3584 - mae: 2.9301 - mse: 16.3584 - val_loss: 23.1440 - val_mae: 3.3218 - val_mse: 23.1440

Epoch 11/60

36/36 - 0s - 8ms/step - loss: 14.8845 - mae: 2.8030 - mse: 14.8845 - val_loss: 22.0320 - val_mae: 3.2148 - val_mse: 22.0320

Epoch 12/60

36/36 - 0s - 8ms/step - loss: 14.1007 - mae: 2.7446 - mse: 14.1007 - val_loss: 21.4347 - val_mae: 3.1709 - val_mse: 21.4347

Epoch 13/60

36/36 - 0s - 8ms/step - loss: 13.5592 - mae: 2.6926 - mse: 13.5592 - val_loss: 20.9801 - val_mae: 3.1183 - val_mse: 20.9801

Epoch 14/60

36/36 - 0s - 8ms/step - loss: 12.8744 - mae: 2.6291 - mse: 12.8744 - val_loss: 20.6138 - val_mae: 3.0929 - val_mse: 20.6138

Epoch 15/60

36/36 - 0s - 8ms/step - loss: 12.5834 - mae: 2.5426 - mse: 12.5834 - val_loss: 20.1067 - val_mae: 3.0289 - val_mse: 20.1067

Epoch 16/60

36/36 - 0s - 8ms/step - loss: 12.2945 - mae: 2.5726 - mse: 12.2945 - val_loss: 20.1485 - val_mae: 2.9954 - val_mse: 20.1485

Epoch 17/60

36/36 - 0s - 8ms/step - loss: 11.6292 - mae: 2.4498 - mse: 11.6292 - val_loss: 19.8272 - val_mae: 3.0280 - val_mse: 19.8272

Epoch 18/60

36/36 - 0s - 8ms/step - loss: 11.7875 - mae: 2.4964 - mse: 11.7875 - val_loss: 19.7747 - val_mae: 2.9893 - val_mse: 19.7747

Epoch 19/60

36/36 - 0s - 8ms/step - loss: 10.8071 - mae: 2.4374 - mse: 10.8071 - val_loss: 19.4899 - val_mae: 2.9394 - val_mse: 19.4899

Epoch 20/60

36/36 - 0s - 8ms/step - loss: 10.5484 - mae: 2.3460 - mse: 10.5484 - val_loss: 19.1290 - val_mae: 2.8710 - val_mse: 19.1290

Epoch 21/60

36/36 - 0s - 8ms/step - loss: 10.2614 - mae: 2.3403 - mse: 10.2614 - val_loss: 19.1074 - val_mae: 2.8635 - val_mse: 19.1074

Epoch 22/60

36/36 - 0s - 8ms/step - loss: 10.0241 - mae: 2.3401 - mse: 10.0241 - val_loss: 19.2033 - val_mae: 2.8503 - val_mse: 19.2033

Epoch 23/60

36/36 - 0s - 8ms/step - loss: 9.9626 - mae: 2.2710 - mse: 9.9626 - val_loss: 18.6036 - val_mae: 2.8252 - val_mse: 18.6036

Epoch 24/60

36/36 - 0s - 8ms/step - loss: 9.6020 - mae: 2.2434 - mse: 9.6020 - val_loss: 18.4747 - val_mae: 2.7770 - val_mse: 18.4747

Epoch 25/60

36/36 - 0s - 8ms/step - loss: 9.5089 - mae: 2.2437 - mse: 9.5089 - val_loss: 18.5592 - val_mae: 2.7752 - val_mse: 18.5592

Epoch 26/60

36/36 - 0s - 8ms/step - loss: 9.1992 - mae: 2.1904 - mse: 9.1992 - val_loss: 18.6239 - val_mae: 2.7469 - val_mse: 18.6239

Epoch 27/60

36/36 - 0s - 8ms/step - loss: 9.0184 - mae: 2.1712 - mse: 9.0184 - val_loss: 18.4458 - val_mae: 2.7831 - val_mse: 18.4458

Epoch 28/60

36/36 - 0s - 8ms/step - loss: 9.2274 - mae: 2.1964 - mse: 9.2274 - val_loss: 18.0883 - val_mae: 2.7530 - val_mse: 18.0883

Epoch 29/60

36/36 - 0s - 8ms/step - loss: 8.8379 - mae: 2.1635 - mse: 8.8379 - val_loss: 18.1416 - val_mae: 2.7474 - val_mse: 18.1416

Epoch 30/60

36/36 - 0s - 8ms/step - loss: 8.6780 - mae: 2.1447 - mse: 8.6780 - val_loss: 18.0183 - val_mae: 2.7820 - val_mse: 18.0183

Epoch 31/60

36/36 - 0s - 8ms/step - loss: 9.1903 - mae: 2.2133 - mse: 9.1903 - val_loss: 18.0481 - val_mae: 2.8027 - val_mse: 18.0481

Epoch 32/60

36/36 - 0s - 8ms/step - loss: 8.4637 - mae: 2.1314 - mse: 8.4637 - val_loss: 17.6470 - val_mae: 2.7634 - val_mse: 17.6470

Epoch 33/60

36/36 - 0s - 8ms/step - loss: 8.5856 - mae: 2.1450 - mse: 8.5856 - val_loss: 17.7953 - val_mae: 2.7016 - val_mse: 17.7953

Epoch 34/60

36/36 - 0s - 8ms/step - loss: 8.1718 - mae: 2.0619 - mse: 8.1718 - val_loss: 17.8786 - val_mae: 2.6658 - val_mse: 17.8786

Epoch 35/60

36/36 - 0s - 8ms/step - loss: 7.8050 - mae: 2.0428 - mse: 7.8050 - val_loss: 17.4320 - val_mae: 2.6921 - val_mse: 17.4320

Epoch 36/60

36/36 - 0s - 8ms/step - loss: 7.7422 - mae: 2.0260 - mse: 7.7422 - val_loss: 17.0421 - val_mae: 2.6534 - val_mse: 17.0421

Epoch 37/60

36/36 - 0s - 8ms/step - loss: 7.7575 - mae: 1.9779 - mse: 7.7575 - val_loss: 17.3632 - val_mae: 2.6220 - val_mse: 17.3632

Epoch 38/60

36/36 - 0s - 8ms/step - loss: 7.6174 - mae: 1.9998 - mse: 7.6174 - val_loss: 16.6116 - val_mae: 2.6319 - val_mse: 16.6116

Epoch 39/60

36/36 - 0s - 8ms/step - loss: 7.5491 - mae: 1.9527 - mse: 7.5491 - val_loss: 17.0154 - val_mae: 2.7230 - val_mse: 17.0154

Epoch 40/60

36/36 - 0s - 8ms/step - loss: 7.6164 - mae: 2.0398 - mse: 7.6164 - val_loss: 17.1923 - val_mae: 2.6671 - val_mse: 17.1923

Epoch 41/60

36/36 - 0s - 8ms/step - loss: 7.3691 - mae: 1.9622 - mse: 7.3691 - val_loss: 16.7006 - val_mae: 2.5751 - val_mse: 16.7006

Epoch 42/60

36/36 - 0s - 8ms/step - loss: 7.0265 - mae: 1.9187 - mse: 7.0265 - val_loss: 16.5408 - val_mae: 2.5706 - val_mse: 16.5408

Epoch 43/60

36/36 - 0s - 8ms/step - loss: 7.0378 - mae: 1.9346 - mse: 7.0378 - val_loss: 16.1454 - val_mae: 2.5522 - val_mse: 16.1454

Epoch 44/60

36/36 - 0s - 8ms/step - loss: 7.0363 - mae: 1.9162 - mse: 7.0363 - val_loss: 16.4976 - val_mae: 2.5639 - val_mse: 16.4976

Epoch 45/60

36/36 - 0s - 8ms/step - loss: 6.7418 - mae: 1.8865 - mse: 6.7418 - val_loss: 16.1442 - val_mae: 2.5754 - val_mse: 16.1442

Epoch 46/60

36/36 - 0s - 8ms/step - loss: 6.6587 - mae: 1.8638 - mse: 6.6587 - val_loss: 16.2308 - val_mae: 2.5458 - val_mse: 16.2308

Epoch 47/60

36/36 - 0s - 8ms/step - loss: 6.8526 - mae: 1.9030 - mse: 6.8526 - val_loss: 15.9731 - val_mae: 2.5638 - val_mse: 15.9731

Epoch 48/60

36/36 - 0s - 8ms/step - loss: 6.7054 - mae: 1.8707 - mse: 6.7054 - val_loss: 16.0701 - val_mae: 2.5394 - val_mse: 16.0701

Epoch 49/60

36/36 - 0s - 8ms/step - loss: 6.4748 - mae: 1.8408 - mse: 6.4748 - val_loss: 15.6880 - val_mae: 2.5163 - val_mse: 15.6880

Epoch 50/60

36/36 - 0s - 8ms/step - loss: 6.4839 - mae: 1.8638 - mse: 6.4839 - val_loss: 16.1445 - val_mae: 2.5782 - val_mse: 16.1445

Epoch 51/60

36/36 - 0s - 8ms/step - loss: 6.1334 - mae: 1.7756 - mse: 6.1334 - val_loss: 15.3155 - val_mae: 2.4964 - val_mse: 15.3155

Epoch 52/60

36/36 - 0s - 8ms/step - loss: 6.0821 - mae: 1.7696 - mse: 6.0821 - val_loss: 15.6474 - val_mae: 2.5117 - val_mse: 15.6474

Epoch 53/60

36/36 - 0s - 8ms/step - loss: 6.0743 - mae: 1.8045 - mse: 6.0743 - val_loss: 14.7500 - val_mae: 2.4915 - val_mse: 14.7500

Epoch 54/60

36/36 - 0s - 8ms/step - loss: 5.7969 - mae: 1.7041 - mse: 5.7969 - val_loss: 15.5576 - val_mae: 2.5976 - val_mse: 15.5576

Epoch 55/60

36/36 - 0s - 8ms/step - loss: 5.9764 - mae: 1.7891 - mse: 5.9764 - val_loss: 15.1105 - val_mae: 2.5220 - val_mse: 15.1105

Epoch 56/60

36/36 - 0s - 8ms/step - loss: 6.0050 - mae: 1.7895 - mse: 6.0050 - val_loss: 15.2569 - val_mae: 2.5354 - val_mse: 15.2569

Epoch 57/60

36/36 - 0s - 8ms/step - loss: 5.6429 - mae: 1.6973 - mse: 5.6429 - val_loss: 14.5583 - val_mae: 2.4487 - val_mse: 14.5583

Epoch 58/60

36/36 - 0s - 8ms/step - loss: 5.5046 - mae: 1.7011 - mse: 5.5046 - val_loss: 15.5672 - val_mae: 2.5913 - val_mse: 15.5672

Epoch 59/60

36/36 - 0s - 8ms/step - loss: 5.8248 - mae: 1.7740 - mse: 5.8248 - val_loss: 14.5579 - val_mae: 2.4877 - val_mse: 14.5579

Epoch 60/60

36/36 - 0s - 8ms/step - loss: 5.9535 - mae: 1.7849 - mse: 5.9535 - val_loss: 14.3759 - val_mae: 2.4764 - val_mse: 14.3759

Step 6 - Evaluate¶

6.1 - Model evaluation¶

MAE = Mean Absolute Error (between the labels and predictions)
A mae equal to 3 represents an average error in prediction of $3k.

In [11]:
score = model.evaluate(x_test, y_test, verbose=0)

print('x_test / loss      : {:5.4f}'.format(score[0]))
print('x_test / mae       : {:5.4f}'.format(score[1]))
print('x_test / mse       : {:5.4f}'.format(score[2]))

x_test / loss      : 14.3759
x_test / mae       : 2.4764
x_test / mse       : 14.3759

6.2 - Training history¶

What was the best result during our training ?

In [12]:
df=pd.DataFrame(data=history.history)
display(df)
loss mae mse val_loss val_mae val_mse
0 552.601074 21.633995 552.601074 459.509033 19.449942 459.509033
1 318.642822 15.401767 318.642822 137.617554 9.121042 137.617554
2 70.639000 6.392056 70.639000 58.648014 5.600778 58.648014
3 39.176506 4.612941 39.176506 41.494419 4.719237 41.494419
4 29.025448 3.932127 29.025448 33.036163 4.149935 33.036163
5 24.005482 3.541128 24.005482 28.892485 3.864979 28.892485
6 21.043699 3.282119 21.043699 26.515785 3.637505 26.515785
7 18.857632 3.125867 18.857632 24.811874 3.524302 24.811874
8 17.190617 3.001753 17.190617 23.708338 3.395098 23.708338
9 16.358448 2.930121 16.358448 23.143991 3.321771 23.143991
10 14.884508 2.803027 14.884508 22.031952 3.214803 22.031952
11 14.100672 2.744578 14.100672 21.434681 3.170895 21.434677
12 13.559190 2.692582 13.559190 20.980061 3.118278 20.980061
13 12.874426 2.629063 12.874426 20.613829 3.092899 20.613829
14 12.583358 2.542602 12.583358 20.106726 3.028854 20.106726
15 12.294549 2.572622 12.294549 20.148535 2.995361 20.148535
16 11.629196 2.449756 11.629196 19.827217 3.028043 19.827217
17 11.787493 2.496351 11.787493 19.774734 2.989304 19.774734
18 10.807133 2.437395 10.807133 19.489931 2.939384 19.489931
19 10.548433 2.346042 10.548433 19.129023 2.871042 19.129023
20 10.261354 2.340328 10.261354 19.107397 2.863487 19.107397
21 10.024061 2.340052 10.024061 19.203321 2.850341 19.203321
22 9.962586 2.270966 9.962586 18.603563 2.825216 18.603563
23 9.601974 2.243445 9.601974 18.474682 2.777019 18.474682
24 9.508885 2.243731 9.508885 18.559206 2.775191 18.559206
25 9.199199 2.190363 9.199199 18.623907 2.746933 18.623907
26 9.018448 2.171181 9.018448 18.445766 2.783106 18.445766
27 9.227386 2.196391 9.227386 18.088251 2.752972 18.088251
28 8.837852 2.163522 8.837852 18.141611 2.747433 18.141611
29 8.677971 2.144674 8.677971 18.018318 2.781960 18.018318
30 9.190325 2.213301 9.190325 18.048130 2.802679 18.048130
31 8.463733 2.131410 8.463734 17.647036 2.763420 17.647036
32 8.585588 2.144973 8.585588 17.795256 2.701603 17.795256
33 8.171778 2.061889 8.171778 17.878607 2.665828 17.878607
34 7.805007 2.042782 7.805007 17.431953 2.692094 17.431953
35 7.742220 2.025972 7.742219 17.042139 2.653405 17.042139
36 7.757503 1.977874 7.757503 17.363218 2.621971 17.363218
37 7.617399 1.999812 7.617400 16.611553 2.631893 16.611553
38 7.549075 1.952750 7.549075 17.015360 2.723044 17.015360
39 7.616443 2.039772 7.616443 17.192270 2.667056 17.192270
40 7.369143 1.962158 7.369143 16.700644 2.575090 16.700644
41 7.026539 1.918651 7.026539 16.540834 2.570634 16.540834
42 7.037803 1.934624 7.037803 16.145403 2.552151 16.145403
43 7.036263 1.916229 7.036263 16.497643 2.563887 16.497643
44 6.741823 1.886532 6.741823 16.144201 2.575377 16.144201
45 6.658704 1.863793 6.658704 16.230818 2.545785 16.230818
46 6.852619 1.902994 6.852619 15.973050 2.563817 15.973050
47 6.705412 1.870660 6.705412 16.070127 2.539413 16.070127
48 6.474781 1.840755 6.474780 15.688000 2.516261 15.688000
49 6.483906 1.863812 6.483906 16.144526 2.578224 16.144526
50 6.133446 1.775570 6.133446 15.315453 2.496422 15.315453
51 6.082084 1.769618 6.082084 15.647402 2.511681 15.647402
52 6.074298 1.804548 6.074298 14.750008 2.491462 14.750008
53 5.796865 1.704091 5.796865 15.557580 2.597581 15.557580
54 5.976436 1.789137 5.976436 15.110455 2.521980 15.110455
55 6.004953 1.789515 6.004953 15.256926 2.535437 15.256926
56 5.642893 1.697277 5.642893 14.558274 2.448738 14.558274
57 5.504644 1.701081 5.504644 15.567157 2.591281 15.567157
58 5.824846 1.774044 5.824846 14.557885 2.487737 14.557885
59 5.953528 1.784931 5.953528 14.375948 2.476415 14.375948
In [13]:
print("min( val_mae ) : {:.4f}".format( min(history.history["val_mae"]) ) )

min( val_mae ) : 2.4487
In [14]:
fidle.scrawler.history( history, plot={'MSE' :['mse', 'val_mse'],
                        'MAE' :['mae', 'val_mae'],
                        'LOSS':['loss','val_loss']}, save_as='01-history')
Saved: ./run/K3BHPD1/figs/01-history_0
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Saved: ./run/K3BHPD1/figs/01-history_1
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Saved: ./run/K3BHPD1/figs/01-history_2
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Step 7 - Make a prediction¶

The data must be normalized with the parameters (mean, std) previously used.

In [15]:
my_data = [ 1.26425925, -0.48522739,  1.0436489 , -0.23112788,  1.37120745,
       -2.14308942,  1.13489104, -1.06802005,  1.71189006,  1.57042287,
        0.77859951,  0.14769795,  2.7585581 ]
real_price = 10.4

my_data=np.array(my_data).reshape(1,13)
In [16]:
predictions = model.predict( my_data, verbose=fit_verbosity )
print("Prediction : {:.2f} K$".format(predictions[0][0]))
print("Reality    : {:.2f} K$".format(real_price))

1/1 - 0s - 4ms/step

Prediction : 10.39 K$
Reality    : 10.40 K$
In [17]:
fidle.end()

End time : 22/12/24 21:21:19
Duration : 00:00:20 215ms
This notebook ends here :-)
https://fidle.cnrs.fr

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